I am also a Mac user who manages a Windows 7 network of 8 clients. I'm currently using WHS Aurora but will be migrating to Amahi this weekend after frustrations with the beta extension and licensing costs (likely to be quite high, out of our budget). Now I'll answer your questions:
Access my network remotely using my Mac when on the road - I would like to be able to VPN into my network and use Microsoft RDP to use my Windows 7 desktop.
There is definitely a VPN built into Amahi. You should be able to do this, although I haven't tested it yet.
Will Amahi's DNS client eliminate the NetBIOS name issues I'm having between Mac and Windows (i.e. I can access a computer via IP but not via NetBIOS name on my Mac)?
I have had trouble with NetBIOS using WHS Aurora. Everything works fine on the Windows 7 clients but the two Mac clients connect to the server VERY slowly. It doesn't matter whether I use the static IP of the server or the name (smb://SERVER). The Macs reconnect after sleep if still in the same IP subnet but fail if used elsewhere and then come back to the office.
Basically, my answer is that I don't know! I will test this as well. My previous experience with Amahi (using Express CD 5.4) was quite positive and the network worked really well. I don't like how Amahi takes over all DNS and DHCP services from my router because that reduces the reliability of the network. But the tradeoff is worth it because of the easy DNS names given to all connected clients.
As for your third question, I don't know. I think Crashplan *might* be able to recover the server from bare metal. Server backup is an essential feature for me too.